In CT X-ray imaging of a patient, X-rays are used to image internal structure and features of a region of the patients body. The imaging is performed by a CT-imaging system, hereinafter referred to as a “CT scanner”, which generally comprises an X-ray source and an array of closely spaced X-ray detectors positioned to face the X-ray source. The X-ray source and array of detectors are mounted in a gantry so that a person being imaged with the CT scanner, generally lying on an appropriate support couch, can be positioned within the gantry between the X-ray source and the array of detectors. The gantry and couch are moveable relative to each other so that the X-ray source and detector array can be positioned axially, along a “z-axis”, at desired locations along the patient's body. The gantry comprises a stationary structure, referred to as a stator, and a rotary element, referred to as a rotor. The rotor is mounted to the stator so that the rotor, is rotatable in a plane perpendicular to the z-axis about a center, referred to as an “isocenter”, of the rotor. The z-axis is usually chosen for convenience to pass through the rotor isocenter so that the rotor rotates about the z-axis.
In third generation CT scanners the X-ray source and detectors are mounted to the rotor. Some, generally older, “single-slice” third generation CT scanners image a region of a patient by imaging a plurality of relatively thin slices of the region, one slice at a time. A single-slice third generation CT scanner comprises a single, generally curved row of detectors located along an arc of a circle that has its plane perpendicular to the z-axis and its center located at a “focal spot” of the scanner's X-ray source. The X-ray source provides a planar, fan-shaped X-ray beam for illuminating the X-ray detectors with X-rays. The fan beam emanates from the focal spot of the X-ray source and is coplanar with the row of X-ray detectors. A vertex angle of the fan beam is referred to as a “fan angle” and a bisector of the fan angle is referred to as an “axis” of the fan beam.
In fourth generation CT scanners, the X-ray detector array comprises detectors positioned around the perimeter of a circle to form a full circle of detectors. The circle of detectors is stationary and the X-ray source is mounted to the rotor and rotates with the rotor. A single-slice fourth generation CT scanner comprises a single circle of X-ray detectors and a fan beam for illuminating the detectors with X-rays. A fourth generation scanner operates similarly to a third generation scanner and the following discussion which generally refers to third generation configurations of CT scanners relates to fourth generation CT scanners as well, with appropriate adjustments readily understood by persons of the art.
In some single slice CT scanners, to image a region of a patient, the patient is moved stepwise along the z direction to “step” the region through the gantry that houses the X-ray source and detector array. Following each step, the X-ray source is rotated around the isocenter to illuminate a thin slice of the region with X-rays from a plurality of different, usually equally spaced angles, referred to as “view angles”. Generally, the X-ray source is rotated through an angle of 360° or (180+Φ) degrees, where Φ is an angular width of the fan angle of the fan beam provided by the X-ray source. A “step and rotate” scan is referred to as an “axial scan”.
At each view angle, each detector in the array of detectors measures intensity of X-rays from the source that pass through the slice along an “attenuation path” from the X-ray source to the detector. The measured intensity provides a value for a line integral of the absorption coefficient of the material along the attenuation path. (The line integral is often, conventionally, referred to as a “Radon transform” but will herein be referred to as a line integral. It is further noted that “line integral data” is alternatively referred to herein also as “line attenuation data”.) The set of line integral values for a slice generated from intensity measurements provided by all the detectors in the detector array for a given view angle of the X-ray source is referred to as a “view” at the view angle.
The set of all the views of the slice is referred to as a “projection” of the slice. A “span” of view angles in a projection refers to an angular difference between a smallest view angle and a largest view angle of views comprised in a projection. For each view angle in a span of a projection, the projection comprises line integrals for a plurality of parallel attenuation paths, each of which passes through the slice at an angle equal to the view angle but at a different distance from the z-axis. A set of line integrals in a projection of a slice for parallel attenuation paths that pass through the slice at an angle equal to a given view angle is referred to as a “parallel” view of the slice at the view angle. In symbols, if the line integral for an attenuation path that passes through the slice at an angle φ and a distance s from the z axis is represented by R(φ,s) and the parallel view at angle φ having N samples is represented by PV(φ,N) then PV(φ,N)={R(φ, s1), R(φ, s2) . . . R(φ, sN)}. To distinguish between a parallel view at a view angle and a view provided by a fan beam at the view angle (for which each attenuation path passes through the slice at different angle) the latter view will hereinafter be referred to as a “fan beam view”.
Let a function “Rφ(s)” of s having a value equal to the line integral R(φ,s) for a given constant angle φ be referred to as a Radon function at the angle φ. It is noted that the Radon functions at view angle φ and (φ+180°) are the same. A convention is therefore used hereinafter that an angle of a Radon function is greater than or equal to 0° and less than 180°. The set of line integrals at different distances s from the isocenter that are comprised in parallel views PV(φ,N) and PV(φ+180°,N) at angles φ and (φ+180°) respectively provide samples for the same Radon function Rφ(s).
To generate an image of a slice from a projection of the slice, each parallel view of the slice provided by the projection is used to generate a Fourier transform of a corresponding Radon function of the slice. The Fourier transforms of the Radon functions provide values for a two-dimensional Fourier transform of the X-ray absorption coefficient of tissue in the slice. The two dimensional Fourier transform is processed in accordance with any of various two-dimensional filtered back projection algorithms known in the art to generate a two dimensional spatial function. The spatial function represents the X-ray absorption coefficient of material in voxels of the slice as a function of position of the voxels. The values for the absorption coefficient for the slice are used to characterize and image tissue in the slice. Values of the absorption coefficient for a plurality of contiguous slices in the region of the patient's body can be used to used to provide a three-dimensional image of internal organs in and features of the region.
Resolution of a CT image of a slice generated from attenuation measurements provided by a CT scanner is a function, inter alia, of a sampling rate at which samples, i.e. line integrals, are acquired for each Radon function of the slice. To an extent that the number of samples acquired for a Radon function increases, a Nyquist sampling rate for the function and a maximum frequency for the Fourier transform of the Radon function increases. As the Nyquist sampling rate increases spatial resolution of the absorption coefficient function and corresponding CT image of the slice increases and approaches an upper limit determined by a size of a cross section of attenuation paths through the slice.
For a fan beam of a CT scanner that is rotated (180°+Φ) about an isocenter located on the fan beam axis, a number of different line integrals provided for each Radon function of the slice is generally equal to the number of detectors in the scanner's detector array. Hereinafter, a fan beam rotated about an isocenter located on the fan beam's axis is said to be “center rotated”. Increasing the angle through which a center rotated fan beam is rotated from (180°+Φ) to 360° does not increase the number of samples acquired for each Radon function of a slice. For a center rotated fan beam, rotated through 360°, X-ray detectors on opposite sides of the fan beam axis provide line integrals for same attenuation paths through the slice. Parallel views of the slice at view angles φ and (φ+180°) provide line integrals for the same attenuation paths through the slice and for the same Radon function Rφ(s).
To double a number of different line integrals acquired for each Radon function of a slice, it is known to offset the fan beam axis from the isocenter and rotate the beam about the isocenter through about 360°. For a fan beam that is “offset rotated” through 360°, X-ray detectors on opposite sides of the fan beam axis provide line integrals for different, generally interleaved, attenuation paths through the slice. In particular a parallel view for a view angle φ and for a view angle (φ+180°) provide different line integrals for a same Radon function Rφ(s). A number of samples for the Radon function Rφ(s) may be doubled by combining the samples provided by the view at view angle φ and at view angle (φ+180°). Doubling the number of different line integrals acquired for each Radon function of the slice doubles the Nyquist sampling rate for the Radon functions of the slice and generally improves resolution of images generated from attenuation measurements acquired with the fan beam.
In some single slice CT scanners a “helical scan” of a patient is performed instead of an axial scan as described above. In a helical scan, a region of a patient to be imaged is continuously advanced through the gantry while the X-ray source simultaneously continuously rotates around the patient and fan beam views of slices in the region are acquired “on the fly”.
The two dimensional filtered back projection algorithms used to generate an image of a slice from “axial scan” line integrals assume that the line integrals of all the fan beam views used to image a slice are for attenuation paths through the patient that are coplanar with the slice. For helical scans, however, no two fan beam views are coplanar. A first fan beam view in a helical scan is displaced along the z-axis from a second fan beam view of the helical scan by a distance determined by the pitch of the helical scan and an angular difference between the view angles of two views. However, usually, for single slice scanners, the pitch of a helical scan is small and for an angular difference of 360° between the view angles of first and second fan beam views, a difference between the z-coordinates of the views is relatively small. As a result, usually, for “helical” single-slice scanners, high resolution, high Nyquist sampling rate data for providing high resolution images can be acquired for each slice using offset rotation of the scanner's fan beam and rotating the beam through 360°.
Modern CT scanners are often multislice scanners designed to simultaneously image a plurality of slices of a patient. A multislice third generation CT scanner comprises a detector array having a plurality of parallel rows of X-ray detectors closely spaced one next to the other along the z-axis direction. The scanner's X-ray source provides a cone shaped beam of X-rays, rather than a planar, fan-shaped X-ray beam for illuminating the X-ray detectors. A multislice fourth generation CT scanner comprises a detector array having a plurality of closely spaced circles of detectors and an X-ray cone beam for illuminating the detectors.
Cone beam geometry may be described with reference to a midplane of the cone beam, which is a plane perpendicular to the z-axis that includes the focal spot of the X-ray source, which generates the cone beam. A vertex angle of the fan-shaped cross section of the cone beam in a plane perpendicular to the midplane that passes through the focal spot is a “cone angle” of the cone beam. For each cone beam view angle a cone beam illuminates a plurality of slices in a region of a patient, where the focal spot of the X-ray source and at least one row of X-ray detectors define each slice. A cone beam view at a given cone beam view angle comprises views acquired with the cone beam for all the slices that the cone beam illuminates at the cone beam angle.
As in the case for single slice scanners, multislice CT scanners can be operated to provide axial scans and/or helical scans of a patient. However, in an axial scan performed by a multislice scanner, the steps are substantially larger than the steps in a single slice scanner. Furthermore, as a cone beam in a multislice scanner is rotated about the z-axis at a fixed z-coordinate, except for views, “midplane views”, acquired from X-rays that propagate in the cone beam midplane, none of the views are coplanar. For a helical scan performed by a multislice scanmer, the pitch of the helical scan is substantially larger than a pitch of a helical scan performed by a single slice scanner. For a helical scan of a multislice scanner, not only are none of the views acquired by the scanner coplanar, but parallel cone beam views acquired by the scanner for view angles differing by 180° are displaced from each other along the z-axis by relatively large distances. In a helical scan performed by a multislice scanner, the midplane of the scanner's cone beam may be displaced along the z-axis by more than 20 mm in a 360° rotation of the scanners' X-ray source. For both axial and helical scans lack of coplanarity increases as the cone beam angle increases.
As a result, for a multislice scanner having a cone beam characterized by a large cone angle data processing schemes conventionally used for processing data from single slice scanners or from small cone angle multislice scanners may introduce overly obtrusive artifacts in images provided by the scanners. In particular prior art methods for combining parallel views at φ and (φ+180°) acquired from 360° offset rotation of the scanner's cone beam to generate “high sampling rate” Radon functions and therefrom an image having enhanced resolution may result in and an unacceptable level of artifacts in the image.
U.S. Pat. No. 5,802,134, the disclosure of which is incorporated herein by reference discloses a nutating slice CT image reconstruction apparatus and method for generating a set of projection data that is used to reconstruct a series of planar image slices. A cone beam image reconstruction algorithm is discussed by Ge Wang, et.al. in an article entitled, “A General Cone-Beam Reconstruction Algorithm; IEEE Transactions on Medical Imaging; Vol. 12. No. 3; September 1993. A method of generating images from cone beam data is presented in an article by Marc Kachelriesz et. al. entitled “Advanced single-slice rebinning in cone beam spiral CT”; Med. Phys. 27 (4); April 2000.